0607 Chapter 6 - Sets and Venn Diagrams

What is a set

A set is a collection of elements

how do we write a set?

curly brackets {}

ξ is the [___] set

universal set (the set of everything)

we use [_____] case letters to represent sets

upper case letters to represent sets (A, B, C, ...) 

we use [_____] case letters to represent elements

lower case letters to represent elements (a, b, c, ...)

n(A) means

number of elements in set A

∈ means

"is an element of"

∉ means

"is not an element of"

∅ means

empty set,  does not contain any elements

a ⊆ b

A is a subset of B: if all elements of the set A are elements of the set B

a ⊄ b

A is not a subset of B

A ∩ B

 the intersection of A and B (the overlap of A and B), This is the set of elements that are in both set A  and set B

A u B

the union of A  and B  (everything in A  or B  orboth)

• This is the set of elements that are in at least one of the sets

• This includes elements in both sets (in the intersection)

A’

The complement of A

• It is the set of all elements in the universal set 

    that are not in A

Venn Diagram A U B

Venn Diagram A∩B

Venn Diagram A’

A∩B’

A’∩B

Venn Diagram A U B’

Venn Diagram A’ U B

Venn Diagram A’ U B’ = (A∩B)’

Venn Diagram A’∩B’ = (A U B)’

Union ( ∪ ):

shade everything in any of the sets.

Intersection ( ∩ ):

shade only the common region(s).

Complement ( A’ ):

shade everything outside the set.

Difference ( A – B = A ∩ B’ ):

shade what’s in A but not in B.

what does what does A ∩ B' mean?

Elements that are in A but not in B

A’ U B

Everything that is not in A, plus everything in B